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\author{Alejandro F. Mac Cawley \and Alex Helminger \and Sergio Maturana}
\title{Life cycle stochastic simulation of a Chilean diary: Economic lessons}
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\begin{abstract}
The dairy producers face
\end{abstract}
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\section{Introduction}

The national dairy sector today faces a new stage whose main features are: high international price fluctuations s, depressed levels of national consumption and excess production that could be ultimately redirected to the external market. In this new scenario new challenges that must be addressed by the different participants in the dairy industry arise.

In t he dairy production systems, as in other agricultural production system s, should take decisions that lead to productive results in the medium and long term. Therefore, due to the lag between action and effect, which uni do the difficult moment that is going through this sector, the count was indispensable tools of economic measures to support decision making of how to analyze the effect of decisions.

Therefore, the objective of this study was to address the problem of the timelessness of decisions by developing and validating a simulation model to determine scenarios against different manej oy market prospects, is it best cuá estrat egia to follow in the long term under certain conditions.

The first part was developed and validated a simulation model for a dairy in the Central Zone of Chile and in the second part the results were analyzed. 

Then an analysis of the current situation and prospects of the domestic dairy industry at the time of the work, the relevance of information systems and particularly the simulation is presented, specifying similar areas in which it has been used and their contribution. 

\section{Dairy market outlook}

As can be seen in Figure 1, the national milk production has doubled since 1989. This trend in increasing domestic production, coupled with a steady decline in international prices has made ​​the prices paid to producers national have decreased considerably.

Importantly, the downward trend that international prices have experienced in the last 5 years has been the result of strong growth in milk production in many exporting and importing countries and the decline in demand for imports due the international economic crisis, as shown in Figure 2, which have a negative impact on the domestic industry.

Low prices and the lowest receiving plants in 2002 compared to 2001, which combined with a national consumption stabilized at 125 liters per capita per year, suggest that the sector is at a crossroads. Was observed that some producers are taking far out of business or sell their milk in an informal market with higher prices due to oversupply and the other causes mentioned above.

This trend is rectified by the information handled in Fedeleche [4] , indicating that in the first quarter of 2003, the situation is even more complicated, accumulating a reduction of 2.3\% compared to the same period 12 months earlier and 4.6\% from that recorded in the production same period two years ago. Notably, during the first quarter, major declines in fresh milk production were recorded in the Eighth and Metropolitan, with 15.1\% and 12.9\%, respectively, the intensive farming systems are those that have suffered more with low price received for milk.

Finally, it is important to note that as of June 2003, should be reflected at the national level, signs of recovery in the prices charged by the industry and involve close the first half of 2003 average price levels similar to those of national first half of 2002 (about 0.16 U.S. \$ per liter). However, this belated reaction of the industry will not be enough to reverse the negative trend in production and in the best case, only help to mitigate it. (Fedeleche, 2003)

In summary, the outlook is not very encouraging, indicating a drop in supply in the coming years, coupled with better pricing internationally, will in the long term retention of the most efficient producers with better conditions and perspectives, with a greater focus on external markets. To be competitive in international markets, companies should have long-term strategies, both from the point of view of investments and technological innovations (Barceló, 1999). 

\section{Literature review}

Within information systems, systems simulation has been used for logistics planning and decision making for over twenty years, increasing each day its responsiveness and significance in business \cite{ramis2002simulation, martinez2011application}. This is corroborated by Shanon (1998), which refers to the simulation as one of the most powerful tools available to decision makers, such as mechanism design and operation of complex systems and processes.

There are many areas where simulation has been important contributions from as diverse as military strategies and games (Proctor and Gubler, 1998) simulations to better serve patients in a clinical (Ramis and Estrada, 2002) areas.

In the agricultural sector, the simulation has been used in various fields. Glen (1987) performed a thorough review of different simulation models: rabbit production systems, system design and production in swine production planning and replacement of dairy cows according to production level, among others. Aguilar (1998) conducted a study to predict milk production of high producing cattle, considering different feeding strategies during lactation. A number of simulation models to assess sustainable production systems are cited by Aguilar (1999) such as: Simulation of root growth, calculation of soil erosion rates of productivity, sustainability of pasture in the high plains of Colombia and sustainability studies production systems of small farmers in Carchi, Ecuador. The same author in his book Simulation Systems (Aguilar, 1997), has different types of simulation models in which different systems of milk production in specific areas are discussed. The common feature of these models is that they do not cover the entire system in the model and which are generally deterministic character (Glen, 1987).

Unlike the above mentioned works, Halachmi develops a model simulation discrete stochastic nature of the optimum design for a mechanized milking room (Halachmi, 2000).

\section{Simulation model of the life cycle of a dairy (MCVL)}

In developing the simulation model, it was possible to determine that the production system had a lot of information available through a software support developed by a company providing the service, which she used to manage in the short term. However, it could display that information was not used to project the workings in the long term and that the decision maker could not determine the effect of today's decisions in the future.

Therefore, we set the goal of this work to generate a model of discrete stochastic nature of simulation, which allow to model the life cycle or mass flow of a dairy long term, determining the most relevant variables. This form of the decision maker could determine with greater information base, the strategies followed by the company, in terms of policy elimination, feeding, reproduction and milk production, seeing its impact in the long term the quantity animals and associated economic outcomes.

The Life Cycle Model of a Dairy (MCVL) separates animals into five main modules, which are circulating throughout the period under study: no Preñada Crianza, Prepartum not pregnant cows, pregnant cows and Dry Cows that deliver the model structure (Figure 3). Each of these modules interact with each other, determining the specific animal behavior within the system. The model in turn has two transition modules, where deliveries of animals (both labor as productive breeding animals) occurs. 

The model data were obtained for a specific month and were processed in a spreadsheet in Excel, separating animals according to age, productive and reproductive status. These data were then injected into the model, starting circ ular by the different modules. This herd composition was obtained, along the period under study and then are processed in a spreadsheet output data from Excel. Simulation model was developed in the software of discrete simulation EXTEND (ImagineThatInc 2000)

Within the model, each individual behaves as a discrete unit cycled within the system changing its attributes as time goes monthly. The inputs, outputs and intermediate actions Known to Occur in each of the modules are summarized in Table 1. 

\subsection{Implementation}

MCVL was implemented in a dairy in central Chile, with along with e l of the property, who contributed their knowledge and together with the management model you determined values ​​to different variables administrator, established the sensitization to perform and validity of the model.

The information used considered a policy of near elimination 30\% focused on animal production, two (high and low production) dietary reasons, first service conception rate of 30\% and an average annual price of \$ 115 pesos per liter. The model was injected with September 2001 data, from which the results for the 10 years under study were obtained s, later validate the model.

In the validation of the model proposed by Law and MacComas (2001) methodology which is followed expert interviews, interacting with the decision maker and the comparison of results generated by MCVL and reality.

Comparing the results with reality was made ​​from a set of data on the composition of the herd monthly Y i, of the company under study, comparing with the data obtained for the same period model X i [7] . Law and Kelton (1991) propose to compare the model with the system by constructing a confidence interval for   = x -  y (mean difference), this being preferable to test the null hypothesis H o =  x =  and, since by definition a model is an approximation of reality, so that in most cases the null hypothesis would be rejected. This is confirmed by Halachmi, who uses this method for validation of the simulation developed for a mechanized milking (Halachmi. 2000) model. By joint F test determined whether the 30 repetitions was well within the established range. 

\section{Results and discussion}

The validation results are shown in summary form in Table 2 appearing in the assay set of F, the null hypothesis is: The model results are similar to the field data, obtained for the whole herd and for each modules (breeding, animal production, and dry milk).

From the results, it may indicate that no significant differences found in the various modules, except for the case of dry animals. The only value that could not be accepted was to dry animals, but its value was very close to the critical value . On the other hand, the percentage of total dry animal herd l is quite low (less than 10\%), indicating that this variable errors do not affect the overall higher mass forms.

A comparison between real and simulated data can be observed in Figure 4. The solid line corresponds to the actual evolution of the number of animals and each of the points corresponding to values ​​obtained for each of the 30 repeated partitions in different months. From the graph it is possible to discern that there is a clear convergence between the data obtained by the model and reality. 

Once validated the model, we proceeded to perform a simulation for 10 years, yielding herd composition for the ten years under study and the economic result. This result is incorporated the costs of feeding, breeding, health and general (according to the stage of the individual).

Net revenues from MCVL for the 10 years under study are presented in Table 4, giving the mean, standard error and confidence interval (95\%) with the lower range (I) and upper (S).

It was determined that according to current driving conditions (CB), the flock was in a growth regime, as can be seen in Table 3. Which is possible to explain the deletion policy presented by the property, less than 30\%. This information is corroborated by Gonzalez and Bas (2002) who mentioned that with greater than 30% removal, herd growth is minimal or even negative. Therefore, the present removal under 30%, you would be facing a growing flock.

Table 4 also shows that there is a decrease in net income in the second year. This decline in revenues associated with the aging form grew more productive animals. L As low then the Net Income is mainly due to higher production costs associated with raising the animals in the system do not provide income.

Importantly, in each simulation variables were kept constant throughout the simulation, ie that there were no variations in price, removal rates, fertility, production variables or other model. This subtraction reliability of long-term predictions, but notwithstanding the above, allows a system evolution in the long run, if the conditions are kept constant. 

\subsection{Sensitivity analysis}

Sensitivities of different disposal policies geared toward productive animals or to animals outside the rearing were performed. High disposal scenarios parenting (AC) and productive (AP) and decreasing the elimination parenting (BC) and production (BP) results are presented. Also the effect of increasing and decreasing the elimination because of infertility both at parenting as the dairy cows were analyzed. The awareness that the removal was increased was termed as Voluntary Added (VA) and it was lower was named Volunteer Baja (VB)., In turn, were sensitized about the average price of milk, establishing two scenarios : High prices and low prices.
 
In turn, changes in the number of more appropriate animal production food rations were performed to determine whether it is more efficient to separate the animals into two or three groups, denoted as RP (which would be the third included serving)

Finally, sensitization was around the reproductive efficiency of the company, analyzing the current situation and what would be the effect of increasing or decreasing the efficiency of fertility (increasing the probability of mating). Sensitization deemed greater efficiency was denoted Countersink Efficient (EE) and Countersink Inefficient (EI) to a lower efficiency. Each of the sensitization is compared with CB being summarized in Table 5. 

Each harbors sensitivities were statistically compared with the base case to determine if the net income for the first year under study were significantly different and therefore if the sensitivities were statistically different. The sensitivities that firieron statistically di base case in the short term were projected for the entire period under study (10 years).

Methodology used was the Fisher F test. Regression was made, specifying the CB as the dependent variable and each independent sensitization as for each of the months and annually for projected for the entire period under study sensitization variables. This was determined in a joint trial if they took the value of 1, allowing demonstrate whether variations in the parameters allowed the results to be statistically different from the CB.

In Figure 5, we can see the increase or diminution of the Net Income of the sensitivities with respect to the CB and its statistical significance that determined which would be projected for ten years. 

Project was considered relevant sensitizations to 10 years were significantly different for all degrees of confidence. In Figure 6 you can see the VPN for 10 years, compared to CB. In addition, the sensitivities of a low and price hike (High and Low) and the effect of adding a third food ration (RP) are included.

As seen in Figure 5, in the short-term challenge with a greater effect on net income corresponded to a rise in price. Importantly, this trend is reversed in the long run, being awareness with greater increases in revenue raising in which the elimination of animal production level, to provide greater longevity and use of animals (Figure 6) was decreased.

Finally is presented in Table 6 the average mass flow for the entire period under study and the average mortality for sensitization and CB. It is noteworthy that both the price and supply variables do not differ to CB Mass Flow as MCVL analyzes these changes at the level of costs and revenues and not on the system itself.

\section{Conclusion}

According to the reviewed literature, there have been some experiences in simulation processes for different production systems, but no simulation that encompasses the entire system for dairy production was found. The proposed model in this paper, between this vision Gondola because it considers the most relevant variables and the production system as a whole. However, the major shortcoming of the model is that it does not suffer feedback parameters over time, as these remain constant over the course of the simulation.

Interestingly, the economic result reflected in net system revenues were lower in the second year under study since according to current disposal policy, there is a greater increase Cattle in the nursery stage regarding productive animals.

L will also economic results indicate that milk production must cease to be the primary criterion in the selection of semen used, emphasizing ma s a functional type that points towards greater longevity. This is evident in the long-term sensitization ( 10 years) in which the largest increases in net income resulting from decreases in mortality rates of productive animals. This is mainly because as the longevity of the animal (via a decrease in the removal rate) is increased, the animal has a longer period over which is productive and hence it can generate income for a longer period.

The results given by the model were generally satisfactory. He could appreciate the importance of reducing the selection pressure level of productive animals, for greater longevity.

He could see the relevance of the price paid for milk in system utilities and third food ration is recommended to minimize system costs.

For future research should include variables such as feed rate endogenously in the model. In this way one could observe an increase in milk production and in other decision variables.

Also, in future improvements MCVL, should consider interactions between different sensitivities to see which produce greater synergy and determine with greater precision which would be the best strategy in the long term and determine how the variables can be regulated in time.

Finally this model can be extended for use as a tool for decision in other dairies, commercial software developed with interaction with the end user, allowing you to analyze the effect on long-term production decisions made ​​today. 

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